The time dependent projection operator method for tunneling in Josephson junctions

1992 ◽  
Vol 89 (2) ◽  
pp. 199-207 ◽  
Author(s):  
Hoang Ngoc Cam ◽  
E. Heiner
Keyword(s):  
Projection Operator ◽  
Josephson Junctions ◽  
Operator Method ◽  
Time Dependent ◽  
Projection Operator Method

Unitary approximations to transition probabilities: Generalized impact parameter theory and the time dependent projection operator method

1984 ◽  
Vol 62 (5) ◽  
pp. 446-453
Author(s):  
Ralph Eric Turner
Keyword(s):  
Impact Parameter ◽  
Projection Operator ◽  
Approximation Scheme ◽  
Transition Probabilities ◽  
Translational Motion ◽  
Operator Method ◽  
Classical Trajectory ◽  
Time Dependent ◽  
Projection Operator Method ◽  
The Impact

A general unitary approximation scheme is presented for transition probabilities based upon the application of the time dependent version of the Zwanzig–Feshbach projection operator method to the generalized impact parameter approximation. The overall approximation scheme is based upon the time dependent picture of the binary collision process. To begin with, the translational and internal motions are decoupled with the translational motion being treated in one of three ways, namely, as a straight line trajectory, as a single curved reference classical trajectory, or as a collection of such trajectories, each of which is associated with a pair of internal states. The internal dynamics is then parameterized by the set of given trajectories which are functions of the impact parameter. This motion is then formally solved using the Zwanzig–Feshbach projection operator method. A set of unitary approximations to these solutions are then presented, based upon a time disordered approximation. These latter approximations are applicable to each of the three treatments of the translational motion. As well, the basis used to describe the internal degrees of freedom may be either atomic or molecular (diabatic or adiabatic). Thus this combined approximation scheme provides a systematic theory for testing various effects associated with either the treatment of the translational motion or the internal motion.

Novel Technique for Quantum-Mechanical Eigenstate and Eigenvalue Calculations based on Seke's Self-Consistent Projection-Operator Method

1997 ◽  
Vol 11 (06) ◽  
pp. 245-258 ◽  
Author(s):  
J. Seke ◽  
A. V. Soldatov ◽  
N. N. Bogolubov
Keyword(s):  
Projection Operator ◽  
Equations Of Motion ◽  
Operator Method ◽  
Approximation Order ◽  
Quantum Mechanical ◽  
Approximation Technique ◽  
Operator Structure ◽  
Projection Operator Method ◽  
Self Consistent ◽  
Effective Hamiltonians

Seke's self-consistent projection-operator method has been developed for deriving non-Markovian equations of motion for probability amplitudes of a relevant set of state vectors. This method, in a Born-like approximation, leads automatically to an Hamiltonian restricted to a subspace and thus enables the construction of effective Hamiltonians. In the present paper, in order to explain the efficiency of Seke's method in particular applications, its algebraic operator structure is analyzed and a new successive approximation technique for the calculation of eigenstates and eigenvalues of an arbitrary quantum-mechanical system is developed. Unlike most perturbative techniques, in the present case each order of the approximation determines its own effective (approximating) Hamiltonian ensuring self-consistency and formal exactness of all results in the corresponding approximation order.

ERRATA: "PHOTOFIELD EMISSION CALCULATIONS BY USING PROJECTION OPERATOR METHOD"

2007 ◽  
Vol 21 (24) ◽  
pp. 1651-1652
Author(s):  
R. K. THAPA ◽  
M. P. GHIMIRE ◽  
GUNAKAR DAS ◽  
S. R. GURUNG ◽  
B. I. SHARMA ◽  
...  
Keyword(s):  
Projection Operator ◽  
Operator Method ◽  
Projection Operator Method
Sign in / Sign up

Export Citation Format

Share Document